Luis C. Dias

An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI

ELECTRE TRI is a well-known method to assign a set of alternatives to a set of predefined categories, considering multiple criteria. Using this method requires setting many parameters, which is often a difficult task. We consider the case where the decision makers (DMs) in the decision process are unsure of which values should each parameter take, which may result from uncertain, imprecise or inaccurately determined information, as well as from lack of consensus among them. This paper discusses the synergy between two approaches developed independently to deal with this difficulty. The first approach infers the value of parameters from assignment examples provided by the DMs, as an elicitation aid. Each assignment example originates mathematical constraints that the parameter values should satisfy. The second approach considers a set of constraints on the parameter values reflecting the imprecise information that the DMs are able to provide. Then, it computes the best and worst categories for each alternative compatible with constraints, in order to present robust conclusions. Both approaches avoid asking for precise values for the parameters. Rather, they proceed to solve the problem in a way that requires from the DMs much less effort. By integrating these two approaches, this paper proposes a new interactive approach, where the insight obtained during robustness analyses guides the DMs during the elicitation phase.

Resolving inconsistencies among constraints on the parameters of an MCDA model

We consider a framework where decision makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the models parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using {0,1} mixed integer linear programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method. � 2002 Elsevier Science B.V. All rights reserved.

ELECTRE TRI for Groups with Imprecise Information on Parameter Values

ELECTRE TRI is a well-known method to assign actions to predefined ordered categories, considering multiple criteria. Using this method requires setting many parameters, which is often a difficult task. We consider the case where a group of Decision Makers (DMs) is unsure of which values each parameter should take, which may result from insufficient, imprecise or contradictory information, as well as from lack of consensus among the group members. In a framework where DMs provide constraints bounding and interrelating the parameter values, rather than fixing precise figures, we discuss the problem of finding the best and worst category that each action may attain.

Valued outranking relations in ELECTRE providing manageable disaggregation procedures

In ELECTRE methods, the construction of an outranking relation amounts at validating or invalidating, for any pair of alternatives (a; b), the assertion ‘‘a is at least as good as b’’. This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the decision makers preferences, accounting for two conditions: concordance and non-discordance. In decision processes using these methods, the analyst should interact with the decision maker in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the decision maker. Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an ‘‘error function’’. Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for outranking methods. Indeed, outranking methods may lead to computationally difficult inference problems. In this paper we are concerned with a slight adaptation of the valued outranking relation used in the ELECTRE III and ELECTRE TRI. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs. � 2003 Elsevier B.V. All rights reserved.

Supporting groups in sorting decisions: Methodology and use of a multi-criteria aggregation/disaggregation DSS

This paper addresses the situation where a group wishes to cooperatively develop a common multicriteria evaluation model to sort actions (projects, candidates) into classes. It is based on an aggregation/disaggregation approach for the ELECTRE TRI method, implemented on the Decision Support System IRIS. We provide a methodology in which the group discusses how to sort some exemplary actions (possibly fictitious ones), instead of discussing what values the model parameters should take. This paper shows how IRIS may be used to help the group to iteratively reach an agreement on how to sort one or a few actions at a time, preserving the consistency of these sorting examples both at the individual level and at the collective level. The computation of information that may guide the discussion among the group members is also suggested. We provide an illustrative example and discuss some paths for future research motivated by this work.

Additive aggregation with variable interdependent parameters: the VIP Analysis software

We consider the aggregation of multicriteria performances by means of an additive value function under imprecise information. The problem addressed here is the way an analysis may be conducted when the decision makers are not able to (or do not wish to) fix precise values for the importance parameters. These parameters can be seen as interdependent variables that may take several values subject to constraints. Firstly, we briefly classify some existing approaches to deal with this problem. We argue that they complement each other, each one having its merits and shortcomings. Then, we present a new decision support software—VIP analysis—which incorporates approaches belonging to different classes. It proposes a methodology of analysis based on the progressive reduction of the number of alternatives, introducing a concept of tolerance that lets the decision makers use some of the approaches in a more flexible manner.

Assessing the performance of biogas plants with multi-criteria and data envelopment analysis

This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators. The comparison of these renewable energy conversion plants is based on two complementary analyses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no information about criteria weights was introduced at the outset. The results suggest that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.

Inferring Electre's veto-related parameters from outranking examples

When considering Electre’s valued outranking relations, aggregation/disaggregation methodologies have difficulties in taking discordance (veto) into account. We present a partial inference procedure to compute the value of the veto-related parameters that best restore a set of outranking statements (i.e., examples that an Electre model should restore) provided by a decision maker, given fixed values for the remaining parameters of the model. This paper complements previous work on the inference of other preference-related parameters (weights, cutting level, category limits, …), advancing toward an integrated framework of inference problems in Electre III and Tri methods. We propose mathematical programs to infer veto-related parameters, first considering only one criterion, then all criteria simultaneously, using the original version of Electre outranking relation and two variants. This paper shows that these inference procedures lead to linear programming, 0–1 linear programming, or separable programming problems, depending on the case.

Evaluation and decision models with multiple criteria: Case studies

This book showcases a large variety of multiple criteria decision applications (MCDAs), presenting them in a coherent framework provided by the methodology chapters and the comments accompanying each case study. The chapters describing MCDAs invite the reader to experiment with MCDA methods and perhaps develop new variants using data from these case studies or other cases they encounter, equipping them with a broader perception of real-world problems and how to overcome them with the help of MCDAs.

Structuring an MCDA model using SSM: A case study in energy efficiency

This work presents the use of a problem structuring method, Soft Systems Methodology (SSM), to structure a Multi-Criteria Decision Analysis (MCDA) model, aimed at appraising energy efficiency initiatives. SSM was useful to help defining clearly the decision problem context and the main actors involved, as well as to unveil the relevant objectives for each stakeholder. Keeneys Value Focused Thinking approach was then used to refine and structure the list of objectives according to the perspective of the main evaluators identified. In addition to describing this particular case study, this paper aims at providing some general guidelines on how SSM may facilitate the emergence of objectives for MCDA models.